?? homming into unit object as sort of "dual", or at least "attempted dual" .... ??? how successful depending in part on whether it's involutory ?? ....

?? though apparently can also consider homming into some other dualizing object ... ??

?? anyway, you can also consider whether sort of "dual" mentioned above (...) is actually adjoint ... ?? one- or two-sided ?? ... and whether automatically so, or almost automatically, needing only some mild additional assumption ... or whatever ... ??? ....

???? non-distirbutivity of egger's semi-/lattice example ... ?? relevance for cocomplete category case ?? ... ???? ..... ???? ....

?? so maybe we should try to figure out whether the prototypical modular-but-not-distributive lattice is self-adjoint as opposed to merely self-dual ... ??? ....

doesn't it seem like it has to be self-adjoint ?? ...

?? did i already make it clear that i'm pretty confused about some stuff here, enough to suspect that i'm probably making some pretty stupid mistakes somewhere ... ?? ...